(x+22)(2+3x)=90

Solution for (x+22)(2+3x)=90 equation:

(x+22)(2+3x)=90

We move all terms to the left:

(x+22)(2+3x)-(90)=0

We add all the numbers together, and all the variables

(x+22)(3x+2)-90=0

We multiply parentheses ..

(+3x^2+2x+66x+44)-90=0

We get rid of parentheses

3x^2+2x+66x+44-90=0

We add all the numbers together, and all the variables

3x^2+68x-46=0

a = 3; b = 68; c = -46;
Δ = b2-4ac
Δ = 682-4·3·(-46)
Δ = 5176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5176}=\sqrt{4*1294}=\sqrt{4}*\sqrt{1294}=2\sqrt{1294}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-2\sqrt{1294}}{2*3}=\frac{-68-2\sqrt{1294}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+2\sqrt{1294}}{2*3}=\frac{-68+2\sqrt{1294}}{6}
$